3rd Quarter Review Momentum Circular Motion
1. Determine the momentum of a ... • 60-kg halfback moving eastward at 9 m/s. • 1000-kg car moving northward at 20 m/s. • 40-kg freshman moving southward at 2 m/s.
1 Answers • p = m * v (60 kg)(9m/s) = 540 kg * m /s B) p = m * v (1000 kg)(20 m/s) 20,000 kg* m/s C) p = m * v 40 kg * 2 m/s 80 kg * m/s
2. A car possesses 20 000 units of momentum. What would be the car's new momentum if ... • its velocity were doubled. • its velocity were tripled. • its mass were doubled (by adding more passengers and a greater load) • both its velocity were doubled and its mass were doubled.
2 answers • 40, 000 units (doubling the velocity will double the momentum) • 60, 000 units (tripling the velocity will triple the momentum • 40, 000 units (doubling the mass will double the momentum) • 80, 000 units (doubling the mass and doubling the velocity will quadruple the momentum)
3. A halfback (m = 60 kg), a tight end (m = 90 kg), and a lineman (m = 120 kg) are running down the football field. Consider their ticker tape patterns below. • Compare the velocities of these three players. How many times greater is the velocity of the halfback and the velocity of the tight end than the velocity of the lineman?
Example 4 • 2. In a phun physics demo, two identical balloons (A and B) are propelled across the room on horizontal guide wires. The motion diagrams (depicting the relative position of the balloons at time intervals of 0.05 seconds) for these two balloons are shown below.
Question 4a • Which balloon (A or B) has the greatest acceleration? Explain.
Answer 4a • Balloon B has the greatest acceleration The rate at which the velocity changes is greatest for balloon B, this is shown by the fact that the speed (distance/time) changes most rapidly.
Example 4B • Which balloon (A or B) has the greatest final velocity? Explain.
Answer 4B • Balloon B has the greatest final velocity. At the end of the diagram, the distance traveled in the latest interval is greatest for Balloon B.
Question 4C • Which balloon (A or B) has the greatest momentum change? Explain.
Answer 4C • Balloon B has the greatest momentum change. The final velocity is greatest for Balloon B, its velocity change is also the greatest. Momentum change depends on velocity change. The balloon with the greatest velocity change will have the greatest momentum change.
Question 4D • Which balloon (A or B) experiences the greatest impulse? Explain.
Answer 4D • The impulse is the same for each car. The impulse equals the momentum change. If the momentum change is the same for each car, then so must be the impulse.
Question 5 • The diagram to the right depicts the before- and after-collision speeds of a car which undergoes a head-on-collision with a wall. In Case A, the car bounces off the wall. In Case B, the car "sticks" to the wall.
Question 5A • In which case (A or B) is the change in velocity the greatest? Explain.
Answer 5A • Case A has the greatest velocity change. The velocity change is -9 m/s in case A and only -5 m/s in case B.
Question 5B • In which case (A or B) is the change in momentum the greatest? Explain.
Answer 5B • Case A has the greatest momentum change. The momentum change is dependent on the velocity change; the object with the greatest velocity change has the greatest momentum change.
Question 5C • In which case (A or B) is the impulse the greatest? Explain.
Answer 5C • The impulse is greatest for Car A. The impulse equals the momentum change. If the momentum change is greatest for car A then the impulse is greatest.
Question 5D • In which case (A or B) is the force which acts upon the car the greatest (assume contact times are the same in both cases)? Explain.
Answer 5D • The impulse is greatest for car A. The force is related to impulse (I = F * t). The bigger impulse for car A is attributed to the greatest force upon car A. Recall that the rebound effect is characterized by larger forces; car A is the car which rebounds.
5. If a 5-kg bowling ball is projected upward with a velocity of 2.0 m/s, then what is the recoil velocity of the Earth (mass = 6.0 x 10^24 kg).
Answer 5 • Since the ball has an upward momentum of 10 kg m/s, the Earth must have a downward momentum of 10 kg m/s. To find the velocity of the Earth, use the momentum equation p = m * v. This equation rearranges to v = p/m. By substituting into this equation • v = (10 kg m/s) / (6 x 10 24 kg). • V = 1.67 * 10 -24 m/s (downward)
7. Would you care to fire a rifle that has a bullet ten times as massive as the rifle? Explain.
Answer 7 • Absolutely not! In a situation like this, the target would be a safer place to stand than the rifle. The rifle would have recoil velocity that is ten times larger than the bullet’s velocity. This would produce the effect of “the rifle actually being the bullet.”
A railroad diesel engine has four times the mass of a flatcar. If a diesel coasts at 5 km/hr into a flatcar that is initially at rest, how fast do the two coast if they couple together?
Train Answer • 4 km/hr
5. A 3000-kg truck moving rightward with a speed of 5 km/hr collides head-on with a 1000-kg car moving leftward with a speed of 10 km/hr. The two vehicles stick together and move with the same velocity after the collision. Determine the post-collision velocity of the car and truck. (CAREFUL: Be cautious of the +/- sign on the velocity of the two vehicles.)
For questions #5-#8: An object is moving in a clockwise direction around a circle at constant speed. Use your understanding of the concepts of velocity and acceleration to answer the next four questions. Use the diagram shown at the right.
5. Which vector below represents the direction of the velocity vector when the object is located at point B on the circle?
Answer 5 • Answer D • The velocity vector is directed tangent to the circle that would be downward when at point B.
6. Which vector below represents the direction of the acceleration vector when the object is located at point C on the circle?
Answer 6 • B The acceleration vector would be directed towards the center that would be up and to the right when at point C
7. Which vector below represents the direction of the velocity vector when the object is located at point C on the circle?
Answer 7 • A The velocity vector would be directed tangent to the circle and that would be upwards at point C.
8. Which vector below represents the direction of the acceleration vector when the object is located at point A on the circle?
Answer 8 • D the acceleration vector would be directed towards the center and that would be straight down when the object is at point A
Example 2 • 2. A 1.5-kg bucket of water is tied by a rope and whirled in a circle with a radius of 1.0 m. At the bottom of the circular loop, the speed of the bucket is 6.0 m/s. Determine the acceleration, the net force and the individual force values when the bucket is at the bottom of the circular loop.
m = 1.5 kg • a = ________ m/s/s • Fnet = _________ N
Answer 2 • F grav = 15 N • a = 36 m/s/s • F net = 54 N Up • F tens = 69 N